Question

The mean deviation from the mean of the discrete data 2, 3, 5, 7, 11, 13, 17, 19, 22 is

• A. 8
• B. 7.5
• C. 5.5
• D. 6

Hint:

The mean deviation from the mean is a measure of dispersion. The process is always: 1. Find the mean. 2. Find the absolute difference of each data point from the mean. 3. Find the average of these absolute differences.

Answer 1

The Correct Option is D

The given data set is $\{2, 3, 5, 7, 11, 13, 17, 19, 22\}$.
Step 1: Calculate the mean ($\bar{x}$) of the data.
Number of observations, $n=9$.
Sum of observations = $2+3+5+7+11+13+17+19+22 = 99$.
Mean, $\bar{x} = \frac{\text{Sum of observations}}{n} = \frac{99}{9} = 11$.
Step 2: Calculate the absolute deviation of each data point from the mean, $|x_i - \bar{x}|$.
$|2 - 11| = 9$
$|3 - 11| = 8$
$|5 - 11| = 6$
$|7 - 11| = 4$
$|11 - 11| = 0$
$|13 - 11| = 2$
$|17 - 11| = 6$
$|19 - 11| = 8$
$|22 - 11| = 11$
Step 3: Calculate the sum of the absolute deviations.
$\sum |x_i - \bar{x}| = 9+8+6+4+0+2+6+8+11 = 54$.
Step 4: Calculate the mean deviation from the mean.
Mean Deviation = $\frac{\sum |x_i - \bar{x}|}{n} = \frac{54}{9} = 6$.